Open clamp structures of the earless type are known in the prior art, for example, as disclosed in my prior U.S. Pat. No. 4,492,004. Though the prior art clamps, as disclosed in this patent, have enjoyed immense commercial success, they may not be able to accommodate at all times the entire tolerance range of the assembly consisting of nipple and hose as specified by the customer. This is so as the clamping band material such as stainless steel frequently used for such clamp structures has relatively low elastic stretchability in the longitudinal direction, which may be inadequate to permit a completely satisfactory clamping action over the entire range of tolerances from the minimum dimension of the hose and of the nipple to the maximum dimension of the hose and of the nipple within their respective tolerance ranges. The problem of tolerance compensation in clamp structures has been recognized already for some time and various solutions have been proposed heretofore. For example, the British Patent 778,861 suggested one or more resilient, arcuately shaped compensating portions. Undulations in the clamping band have been proposed in the French Patent 2,470,275 and can also be found in U.S. Pat. Nos. 4,308,648 and 4,919,682. However, to avoid any leakage underneath the undulations, it was necessary to cover the same by the full band width of the inner band portion. Adopting the teachings of the British Patent 1,064,048, the European Patent 0 296 918 suggested to offset undulations located on opposite sides of a central cut. However, the problem remained with these prior art proposals of assuring an internal clamping surface devoid of any steps, offsets or discontinuities. Moreover, the need to cover the undulations with the full-width inner band portion of the clamping band resulted in increased cost owing to the increased length of the clamping band required under these circumstances. Additionally, undulations also involve some cost considerations as regards the requisite length of clamping band in the clamp structure. Other proposals to provide some increased elastic stretchability of the clamping band involved cut-outs in the clamping band. For example, zig-zag shaped cut-outs in the band to impart some elasticity were suggested in U.S. Pat. No. 1,705,895. Other configurations in the clamping band for similar purposes can be found in U.S. Pat. No. 4,910,832 and German Patent DE 30 18 383 as also in my own prior U.S. Pat. No. 4,987,651 which disclosed concavely shaped lateral band portions enclosing therebetween an at least approximately hourglass-shaped opening. Common to all of these last-mentioned prior art proposals is the fact that they require movement of band portions, not only in the direction of the tensional forces, i.e., in the longitudinal direction of the clamping band, but also in a direction transverse thereto as they undergo deformation in the presence of tensional forces.